Solving moment and polynomial optimization problems on Sobolev spaces
Résumé
Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares hierarchy, allowing to numerically solve non-convex polynomial optimization problems on infinite-dimensional Sobolev spaces with global convergence guarantees
Domaines
Optimisation et contrôle [math.OC]Origine | Fichiers produits par l'(les) auteur(s) |
---|